Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&68\\22&9\end{bmatrix}$, $\begin{bmatrix}33&14\\100&47\end{bmatrix}$, $\begin{bmatrix}36&71\\17&6\end{bmatrix}$, $\begin{bmatrix}86&117\\33&110\end{bmatrix}$, $\begin{bmatrix}103&96\\88&107\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.3.sy.4 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $192$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.1-24.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 60.96.0-60.c.4.3 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.96.0-60.c.4.23 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.96.1-24.iu.1.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.2-120.h.2.4 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.h.2.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.384.5-120.qp.1.12 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.re.3.15 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.ux.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.vb.2.11 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.vl.1.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.vn.4.9 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.yt.3.1 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.yy.4.9 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.baj.3.11 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bal.1.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.baz.3.11 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bbb.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bcv.4.9 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bcx.2.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bdl.4.9 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.bdn.3.1 | $120$ | $2$ | $2$ | $5$ |